Quark-hadron duality and parity violating asymmetry of electroweak reactions in the Δ region

A dynamical model [T. Sato and T.-S. H. Lee, Phys. Rev. C 54, 2660 (1996); 63, 055201 (2001); T. Sato, D. Uno, and T.-S. H. Lee, ibid. 67, 065201 (2003)] of electroweak pion production reactions in the {delta}(1232) region has been extended to include the neutral current contributions for examining the local quark-hadron duality in neutrino-induced reactions and for investigating how the axial N-{delta} form factor can be determined by the parity violating asymmetry of N(e{sup {yields}},e{sup '}) reactions. We first show that the recent data of (e,e{sup '}) structure functions F{sub 1} and F{sub 2}, which exhibit the quark-hadron duality, are in good agreement with our predictions. For possible future experimental tests, we then predict that the structure functions F{sub 1},F{sub 2}, and F{sub 3} for ({nu},e) and ({nu},{nu}{sup '}) processes also show the similar quark-hadron duality. The spin-dependent structure functions g{sub 1} and g{sub 2} of (e,e{sup '}) have also been calculated from our model. It is found that the local quark-hadron duality is not seen in the calculated g{sub 1} and g{sub 2}, while our results for g{sub 1} and some polarization observables associated with the exclusive p(e{sup {yields}},e{sup '}{pi}) and p{sup {yields}}(e{sup {yields}},e{sup '}{pi}) reactions aremore » in reasonably good agreement with the recent data. In the study of parity violating asymmetry A of N(e{sup {yields}},e{sup '}) reactions, the relative importance between the nonresonant mechanisms and the {delta} excitation is investigated by taking into account the unitarity condition. Predictions are made for using the data of A to test the axial N-{delta} form factors determined previously in the studies of N({nu}{sub {mu}},{mu}{sup -}{pi}) reactions. The predicted asymmetry A are also compared with the parton model predictions for future experimental investigations of quark-hadron duality.« less